Solving a Production Scheduling Problem by Means of Two Biobjective Metaheuristic Procedures

Near optimal and optimal solutions for an integrated employee timetabling and production scheduling problem

The main scope of this paper is the implementation of a method for production scheduling, using advanced model checking tools. This method makes use of timed automata to model complex production scheduling problems such as the job-shop and the open-shop scheduling problems. By modelling scheduling problems using timed automata, feasible schedules correspond to paths in the automata, while finding the optimum schedule corresponds to finding the shortest path in an automaton. Several algorithms and heuristics have been proposed for finding the shortest paths in timed automata, which are mainly based on the implementation of graph algorithms that search the transition graph. In our work, an advanced model design and checking tool, called UPPAAL, has been used to implement and test the above method on a number of different models and to show the effectiveness of such an approach in terms of finding optimal or near to optimal, schedules in polynomial time, even for large-scale problems.

PurposeProper management of supplies and their delivery greatly affects the competitiveness of companies. This paper aims to propose an integrated decision-making approach for integrated transportation and production scheduling problem in a two-stage supply chain. The objective functions are minimizing the total delivery tardiness, production cost and the emission by suppliers and vehicles and maximizing the production quality.Design/methodology/approachFirst, the mathematical model of the problem is presented. Consequently, a new algorithm based on a combination of the genetic algorithm (GA) and the VIKOR method in multi-criteria decision-making, named GA-VIKOR, is introduced. To evaluate the efficiency of GA-VIKOR, it is implemented in a pharmaceutical distribution company located in Iran and the results are compared with those obtained by the previous decision-making process. The results are also compared with a similar algorithm which does not use the VIKOR method and other algorithm mentioned in the literature. Finally, the results are compared with the optimized solutions for small-sized problems.FindingsResults indicate the high efficiency of GA-VIKOR in making decisions regarding integrated production supply chain and transportation scheduling.Research limitations/implicationsThis research aids the manufacturers to minimize their total delivery tardiness and production cost and at the same time maximize their production quality. These improve the customer satisfaction as a part of social and manufacturer’s power of competitiveness. Furthermore, the emission minimizing objective functions directly provides benefits to the environment and the society.Originality/valueThis paper investigates a new supply chain scheduling the problems and presents its mathematical formulation. Moreover, a new algorithm is introduced to solve the multi-objective problems.

Matheuristic is an optimisation methodology that integrates mathematical approaches and heuristics to address intractable combinatorial optimisation problems, where a common framework is to insert mixed integer linear programming (MILP) models as local search functions for evolutionary algorithms. However, since a mathematical programming formulation only tries to find the solution with the best objective value, matheuristics are rarely adopted to multi‐objective scenarios asking for a set of Pareto optimal solutions, for example, vehicle routing problems and production scheduling problems. In this situation, the ɛ ‐constraint, which transforms multi‐objective problems into single‐objective formulations by considering selected objectives as constraints, seems to be a promising approach. First, an augmented ɛ ‐constraint‐based matheuristic methodology ( ɛ ‐MH) is proposed to apply the idea of ɛ ‐constraint to embedded MILP models, so that Pareto fronts obtained by meta‐heuristics can be further improved by solving a set of MILP models. Afterwards, four speed‐up strategies are developed to alleviate the computational burden resulting from repeatedly solving mathematical formulations, which also imply preferable scenarios for taking advantages of the ɛ ‐MH. Finally, several real‐world bi‐objective scheduling problems are discussed to present potential applications for the proposed methodology.

An Open-Pit Production Scheduling (OPPS) problem focuses on specifying block production scheduling to achieve the highest possible Net Present Value (NPV). This paper presents a new mathematical model for OPPS under uncertainty. To this end, a robust box and ellipsoidal counterpart approach was used. The proposed method was implemented in a hypothetical model. A Genetic Algorithm (GA) and an exact mathematical modeling approach were used to solve the model. It was shown that the scheduling of deterministic and robust models in various conditions is different. Considering the type of robust counterparts, different production plans under various conditions were scheduled. Furthermore, the price of robustness was determined for various levels of conservation.

In a factory of automobile component primer painting, various automobile parts are attached to overhead hangers in a conveyor line and undergo a series of coating processes. Thereafter, the components are wrapped at a packaging station. The packaging process should be fully balanced by an appropriate sequence of components to prevent the bottleneck effect because each component requires different packaging times and materials. An overhead hanger has a capacity limit and can hold varying numbers of components depending on the component type. Capacity loss can occur if the hanger capacity is not fully utilized. To increase hanger utilization, companies sometimes mix two or more component types on the same hangers, and these hangers are called mixed hangers. However, mixed hangers generally cause heavy workload because different items require additional setup times during hanging and packing processes. Hence, having many mixed hangers is not recommended. A good production schedule requires a small number of mixed hangers and maximizes hanger utilization and packaging workload balance. We show that the scheduling problem is NP-hard and develop a mathematical programming model and efficient solution approaches for the problem. When applying the methods to solve real problems, we also use an initial solution-generating method that minimizes the mixing cost, set a rule for hanging the items on hangers considering eligibility constraint, and decrease the size of tabu list in proportion to the remaining computational time for assuring intensification in the final iterations of the search. Experimental results demonstrate the effectiveness of the proposed approaches.

PurposeIn order to achieve excellence in manufacturing, goals like lean, economic and quality production with enhanced productivity play a crucial role in this competitive environment. It also necessitates major improvements in generally three primary technical areas: variation reduction, equipment reliability, and production scheduling. Complexity of the real world scheduling problems also increases with interactive multiple decision‐making criteria. This paper aims to deal with multi‐objective flow shop scheduling problems, including sequence dependent set up time (SDST). The paper also aims to consider the objective of minimizing the weighted sum of total weighted tardiness, total weighted earliness and makespan simultaneously. It proposes a new heuristic‐based hybrid simulated annealing (HSA) for near optimal solutions in a reasonable time.Design/methodology/approachSix modified NEH's based HSA algorithms are proposed for efficient scheduling of jobs in a multi‐objective SDST flow shop. Problems of up to 200 jobs and 20 machines are tested by the proposed HSA and a defined relative percentage improvement index is used for analysis and comparison of different MNEH's based hybrid simulated annealing algorithms.FindingsFrom the results, it has been derived that performance of SA_EWDD (NEH) up to ten machines' problems, and SA_EPWDD (NEH) up to 20 machines' problems, were better over others especially for large sized SDST flow shop scheduling problems for the considered multi‐objective fitness function.Originality/valueHSA and multi‐objective decision making proposed in the present work is a modified approach in the area of SDST flow shop scheduling.

We address a novel integrated maintenance and production scheduling problem in a multi-machine and multi-period production system, considering maintenance as a long-term decision. Deterioration of machines over time decreases production capacity. Since maintenance activities not only improve machine conditions, increasing production capacity, but also take time that cannot be used for production, the challenge is to assign maintenance to periods and to schedule maintenance and production activities within each period to minimize the combined cost of maintenance and lost production over the planning horizon. Motivated by logic-based Benders decomposition, we design an integrated two-stage algorithm to solve the problem. The first stage assigns maintenance to machines and time periods, abstracting the scheduling problem, while the second stage creates a schedule for the current time period. The first stage is then re-solved using feedback from the schedule. This iteration between maintenance planning and scheduling continues until the solution costs in two stages converge. The integrated approach models the interdependencies between maintenance and scheduling decisions in highly coupled processes such as wafer fabrication in the semiconductor manufacturing. Our results demonstrate that the benefit of integrated decision making increases when maintenance is less expensive relative to lost production cost and that a longer horizon for maintenance planning is beneficial when maintenance cost increases.

Presents the master production scheduling (MPS) problem of a flexible manufacturing system (FMS). Earliness/tardiness production scheduling and planning (ETPSP) is one of the solutions used to integrate MRP and JIT effectively. Previous researches on ETPSP have only applied to problems of single/parallel machines with earliness and tardiness penalties on a common due date and capacity. Proposes a revised ETPSP for the purpose of developing an MPS that can fit into the FMS environment where a multiple machine capacity on multi‐processes and batch sizes is included. Outlines the application of an enhanced ETPSP method using a genetic algorithm (GA) solution to solve a multi‐product FMS production problem. Shows that the use of the improved ETPSP model can represent a real life FMS environment and that a solution can be effectively and efficiently obtained using the GA approach.

Operation scheduling for a class of production systems with “instantly consumed” products is very important. It is challenging to satisfy the real time system demand and to consider the realizability of the production schedules. This paper formulates a new model for optimization based production scheduling problems with integral constraints. Based on the detailed analysis of the production rate constraints, it is proved that this type of optimization problems is equivalent to a smooth nonlinear programming problem. The reachable upper and lower bounds of the production amount in every period can be expressed as functions of two variables, i.e., the production rate at the start and end of that period. It is also proved that the gradients of these functions are monotonic, and their convexity or concavity is guaranteed. When the production cost function is convex, this type of optimization problems is equivalent to a convex programming problem. With the above analysis, a two-stage solution method is developed to solve the production scheduling problems with integral constraints, and in many applications the global optimal solution can be obtained efficiently. With the new model and solution method, the difficulties caused by the constraints on production rate can be overcome and the optimal schedule can be obtained with the real time system demand satisfied. Numerical testing for scheduling of electric power production systems is performed and the testing results are discussed. It is demonstrated that the new model and solution method are effective.

This research proposes a two-layered supply chain model consisting of a set of clients and suppliers for dynamic supply chain management considering production and transportation scheduling problems. The model provides a method to optimize both production schedules and transportation schedules simultaneously, in order to estimate suitable prices and delivery times of products. A prototype of simulation system for dynamic supply chain management was developed and some computational experiments were carried out in order to verify the effectiveness of the model. Experimental results show that the prototype system is available to determine suitable production schedules and transportation schedules from the viewpoint of the number of contracted orders and the cost for wasteful shipping.

This article reviews the production scheduling problems focusing on those related to flexible job-shop scheduling. Job-shop and flexible job-shop scheduling problems are one of the most frequently encountered and hardest to optimize. This article begins with a review of the job-shop and flexible job-shop scheduling problem, and follow by the literature on artificial immune systems (AIS) and suggests ways them in solving job-shop and flexible job-shop scheduling problems. For the purposes of this study, AIS is defined as a computational system based on metaphors borrowed from the biological immune system. This article also, summarizes the direction of current research and suggests areas that might most profitably be given further scholarly attention.

Detailed scheduling of batch production in a cell with parallel facilities and common renewable resources

This paper deals with the problem of production scheduling in a two-stage hybrid flow shop, which consists of one machine in the first stage, and multiple process lines in the second stage. In the first stage, materials are batch-processed, which are then fed into one of several process lines in the second stage, depending on the final product specifications. First, we formulated the total flow time or makespan, the capacity utilization and the maximum work-in-process level as measures of manufacturing performance. We analysed, through a series of numerical experiments, how these performance measures are affected by lot sizing, sequencing rules and the scheduling scenario. The following points were clarified. (1) The ratio rule yields the best performance with regard to the makespan, but the LPT rule yields the best performance with regard to the maximum work-in-process level, (2) The optimum lot size is also affected by such operation conditions as the unit processing time, the setup time, and the ratio ...

The problem of production and employment scheduling may be stated as follows. Given the monthly demands for the product turned out by a factory, what should be the monthly production rates and work force levels in order to minimize the total cost of regular payroll and overtime, hiring and layoffs, inventory and shortages incurred during a given planning interval of several months? This problem has received a classical solution in two papers by Holt, Modigliani, Muth, and Simon (Holt, C. C., F. Modigliani, H. A. Simon. 1955. A linear decision rule for production and employment scheduling. Management Sci. (October); Holt, C. C., F. Modigliani, J. F. Muth. 1956. Derivation of a linear decision rule for production and employment. Management Sci. (January).). These authors assumed quadratic cost functions. Their treatment of the problem will be referred to as “quadratic programming.” It appears, however, that in the majority of practical applications and theoretical models the cost functions are assumed to be linear. It, therefore, seems desirable to have a method of solution for the linear case as well. In this paper it is shown that a solution can be obtained by linear programming methods. From the linear programming viewpoint, this paper is of an expository nature. Management Technology, ISSN 0542-4917, was published as a separate journal from 1960 to 1964. In 1965 it was merged into Management Science.